I feel the murder went this way, Neff received a call that morning telling him someone needed help or whatever, possibly why he went to auto parts store. The two thiefs went to Joe's house, either before or after Joe was surprised at the bar by the third. Somehow the safe's combination was found either before or after Joe was killed and telephoned to the other two in the house, who opened and took the money. They went back to the bar and loaded the body in a pickup truck, one man on both sides of the body and a third holding the legs, covering it with a tarp. From there they drove the back way thru Cameron, into Pocola and dropped the body at the strip pits, from there the may have went the back way into Spiro and back to Poteau on 59 South.
This explains the short time line and how it had to have happened